Flatness and thickness variation of test pieces can be measured optically by evaluating interference patterns produced between paired surfaces. The flatness of a surface is compared to a reference surface. Thickness variation is compared between two surfaces of a test piece. Grazing incidence interferometry, where at least one of the paired surfaces is illuminated at non-normal angles of incidence, provides for enhancing specular reflectivity and for adjusting the sensitivity of the measurements.
Interferometric measurements of thin transmissive test pieces present special problems, because opposite surfaces of the transmissive test pieces can participate in forming multiple interference patterns. For example, interference patterns can be formed between each of the opposite surfaces and a common reference surface as well as between the opposite surfaces themselves. Each of the interference patterns contains information about the test piece, but the information is obscured when the interference patterns overlie each other.
In the grazing incidence interferometer of co-assigned U.S. Pat. No. 4,325,637 to Moore, which is hereby incorporated by reference, spatial coherence of the illuminating beam is limited to exclude interference patterns between surfaces separated beyond a coherence limit. Collimated light reflected from the surfaces laterally shears as a function of the separation between the surfaces. A rotating diffuser interrupts the illuminating beam and reduces spatial coherence so that interference fringes do not form between surfaces separated by more than the distance between intended test and reference surfaces.
However, reduced spatial coherence does not preclude interference fringes from forming between the opposite surfaces of thin transmissive test pieces, whose opposite surfaces are separated by amounts comparable to the separation between the transmissive optic and a reference surface. A first interference pattern measuring flatness is formed between the reference surface and the closest of the opposite test surfaces of the test piece. A second overlying interference pattern measuring thickness (and index) variation is formed between the opposite surfaces of the test piece. A third overlying interference pattern also measuring flatness can be formed (if also within the coherence limit) between the reference surface and the more remote of the opposite surfaces of the test piece. The overlying interference patterns obscure the different flatness or thickness variation information contained within each pattern.
Our invention provides for distinguishing among superimposed interference patterns that are formed by a grazing incidence interferometer between paired combinations of a reference surface and two nominally parallel surfaces of a thin transmissive test piece. The grazing angle of the illuminating beam, which is incident upon both the test piece and the reference surface, is varied in a stepwise manner to elicit distinguishing responses from the superimposed interference patterns. The distinguishing responses enable the evaluation of individual interference patterns.
An exemplary method of measuring a transmissive plane parallel test piece with a grazing incidence interferometer includes reflecting a beam of light at a non-normal grazing angle from both a reference surface and two nominally parallel surfaces of the transmissive test piece. A first interference pattern formed between the reference surface and one of the two nominally parallel surfaces of the test piece is superimposed upon a second interference pattern formed between the two nominally parallel surfaces of the test piece. To distinguish between the first and second interference patterns, the non-normal grazing angle of the beam is varied through a range of angles at which local fringe intensities of each of the superimposed interference patterns shift through at least one cycle. A modulation frequency at which the local fringe intensities shift within one of the superimposed interference patterns is determined. The local fringe intensities varying at the modulation frequency are evaluated to extract phase information from the one interference pattern.
For measuring the flatness of one of the nominally parallel surfaces of the test piece, the determined modulation frequency is the modulation frequency at which the local fringe intensities shift within the first interference pattern. For measuring thickness variation between two nominally parallel surfaces of the test piece, the modulation frequency is the modulation frequency at which the local fringe intensities shift within the second interference pattern. The modulation frequencies of both the first and second interference patterns can be determined to evaluate both the flatness and the thickness variation of the test piece surfaces.
Preferably, the non-normal grazing angle is progressively varied through different size angular increments corresponding to approximately even increments of optical path difference between the surfaces evaluated by the one interference pattern. The resulting modulation frequencies remain constant throughout the range of tilt (i.e., the range of grazing angles) for both the interference patterns. However, the modulation frequencies associated with the first and second interference patterns differ as a function of the separation between the surfaces that form them.
Differences between the modulation frequencies of the superimposed interference patterns can be enhanced by adjusting the non-normal grazing angle and the separation between the test piece and the reference surface. The modulation frequency is preferably calculated independently of the step of varying the non-normal grazing angle based on an expected relationship between the test piece and the grazing incidence interferometer.
The beam of light is preferably a temporally coherent beam of spatially coherent-limited light. Shear produced between the various reflections from the reference surface and the two nominally parallel surfaces of the test piece is a function of both the non-normal grazing angle and spacing between the surfaces. A first of the two nominally parallel surfaces of the test piece is oriented adjacent to the reference surface, and a second of the two nominally parallel surfaces is oriented remote from the reference surface. The shear between the reflections from the reference surface and the second of the two nominally parallel surfaces is preferably beyond a spatial coherence limit within which the interference patterns are formed.
Overall, our preferred method exploits the results of a non-normal grazing angle variation to distinguish among superimposed interference patterns produced between paired combinations of a reference surface and two nominally parallel surfaces of a transmissive test piece. A modulation frequency is calculated for a shift of local fringe intensities of one of the superimposed interference patterns as a function of the variations in the non-normal grazing angle at which a light beam producing the interference patterns reflects from the reference surface and the two nominally parallel surfaces of the transmissive test piece. The non-normal grazing angle of the beam is varied through a range of angles at which local fringe intensities of each of the superimposed interference patterns shift through at least one cycle. A succession of superimposed fringe-shifted forms of the interference patterns is produced throughout the range of angles at which the non-normal grazing angle of the beam is varied. Local fringe intensities that progressively vary through the succession of fringe-shifted forms of the interference patterns at the calculated modulation frequency are distinguished from other local fringe intensities that do not similarly vary at the same modulation frequency.
The modulation frequency at which the local fringe intensities shift within one of the superimposed interference patterns is preferably calculated in advance of the production of the superimposed interference patterns based on information known about the test piece and its relationship to the grazing incidence interferometer. The calculation preferably identifies modulation frequencies for both of the superimposed interference patterns, and these modulation frequencies distinguish the progressive variations in local fringe intensities between the two superimposed interference patterns.
Calculating the modulation frequencies in advance of the actual measurements produces more consistent results for measuring similar test pieces by eliminating noise distortions than accompany the actual measurements. The noise distortions can make the true modulation frequencies more difficult to distinguish among other frequencies associated with the noise, especially from a limited number of the fringe-shifted forms of the interference patterns. However, once the modulation frequencies are determined (e.g., by pre-calculation), the progressive variations in the local fringe intensities associated with the different interference patterns can be more easily recognized at the modulation frequencies from a more limited number of the fringe-shifted forms of the interference patterns.